ˆ An Introduction to Symplectic Geometry, R. Berndt, ˆ Lecture notes: Symplectic Geometry, S. Sabatini, Sommersemester , Uni-. , English, Book edition: An introduction to symplectic geometry [electronic resource] / Rolf Berndt ; translated by Michael Klucznik. Berndt, Rolf, An Introduction to Symplectic. Geometry. Rolf Berndt. Translated by. Michael Klucznik. Graduate Studies in Mathematics. Volume American Mathematical.

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Libraries and resellers, please contact cust-serv ams. See our librarian page for additional eBook ordering options. Graduate Studies in Mathematics Volume: Symplectic geometry is a central topic of current research in mathematics.

An Introduction to Symplectic Geometry (Graduate Studies in Mathematics 26) – PDF Free Download

Indeed, symplectic methods are key ingredients in the study of dynamical systems, differential equations, algebraic geometry, topology, mathematical physics and representations of Lie groups. This book is a true introduction to symplectic geometry, assuming only a general background in analysis and familiarity with linear algebra.

It starts with the basics of the geometry of symplectic vector spaces. Then, symplectic manifolds are defined and explored.


In addition to shmplectic essential classic results, such as Darboux’s theorem, more recent results and ideas are also included here, such as symplectic capacity and pseudoholomorphic curves. These ideas have revolutionized the subject.

An Introduction to Symplectic Geometry (Graduate Studies in Mathematics) by Rolf Berndt

Further principal ideas are carefully examined, such as Hamiltonian vector fields, the Poisson bracket, and connections with contact manifolds. Berndt describes some of the close connections between symplectic geometry and mathematical physics in the last two chapters of the book.

In particular, the moment map is defined and explored, both mathematically and in its relation to physics. He also introduces symplectic reduction, which is an important tool for reducing the number of variables in a physical system and for constructing new symplectic manifolds from old.

The final chapter is on quantization, which uses symplectic methods to take classical mechanics to quantum mechanics. This section includes a discussion of the Heisenberg group and the Weil or metaplectic representation of the symplectic group.

Several appendices provide background material on vector bundles, on cohomology, and on Lie groups and Lie algebras and their representations. Berndt’s presentation of symplectic geometry is a clear and concise introduction to the major methods and applications of the subject, and requires only a minimum of prerequisites.


An Introduction to Symplectic Geometry (Graduate Studies in Mathematics 26)

This book would be an excellent text for a graduate course or as a berndg for anyone who wishes to learn about symplectic geometry. Join our email list.

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An Introduction to Symplectic Geometry. Author s Product display: University of Hamburg, Hamburg, Germany. Graduate Studies in Mathematics.

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